Here we consider two atoms moving
in a circular orbit and weakly interacting with the massive scalar field. The
frequency of the field in Eq. (REF ) is given by, \(E_k=\sqrt{k^2+m^2}\) .
Two-point correlation function of the massive scalar field is
[1]},
\(G(x,x^{\prime })&\equiv & \langle 0|\hat{\Phi }(t,x) \hat{\Phi }(t^{\prime },x^{\prime })|0\rangle \nonumber \\& =& \int \frac{d^4k}{(2\pi )^{\frac{3}{2}}} \delta (k^2-m^2)e^{-ik(x-x^{\prime })}~,\nonumber \\&=&-\frac{m}{4\pi ^2}\frac{K_1 \big (m \sqrt{(t-t^{\prime }-i\epsilon )^2-(x-x^{\prime })^2}\big )}{\sqrt{(t-t^{\prime })^2-(x-x^{\prime })^2}}~.\nonumber \\\) 
